I had the (self-inflicted) problem of modeling systems of linear equations in C#. `x` is a Sym, `x+2` is an Expr, `[2x,3y]` is a TermVector, etc. I wanted the c

I had the (self-inflicted) problem of modeling systems of linear equations in C#. `x` is a Sym, `x+2` is an Expr, `[2x,3y]` is a TermVector, etc. I wanted the comforts of NumPy, so adding an Int to a SymVector should make an ExprVector by broadcast, you should be able to multiply two IntMatrixes together but not two SymMatrixes (since that's not linear), etc. It would have been a lot of wrapper code to write. Instead, I implemented a minimal set of primitives, and wrote a set of derivation rules (e.g. "if you have X+Y, and Y supports negation, you can derive X-Y by X+(-Y)"), and constraints (operator overloads mustn't have ambiguous signatures, no cycles allowed in the call tree), and set up a code generator. 250 lines of Prolog, plus another 250 of ASP (a dialect of Prolog), and I had a code synthesizer. it was one of the most magical experiences of my entire career. I'd write an optimized version of a function, rerun synthesis and it would use it everywhere it could. I'd add new types and operators and it'd instantly plumb them through. seeing code synthesis dance for you feels amazingly liberating. it's like the opposite of technical debt.